Aircraft: B737
Phase of flight: Takeoff / Launch
Anomaly: Conflict Ground Conflict; Less Severe; Ground Event / Encounter Object; Ground Excursion Runway

Local show time was approximately XA:00. This was 55 minutes prior to scheduled takeoff time. (XA:55Z). Airfield conditions were night operations with no visibility issues. Upon arriving at the aircraft at gate; maintenance informed us of a write up requiring deferment (Auto Speed Brake System). There was also a problem with the Captain's seat belt. The maintenance issues lead to a block out time of XB:45Z (:50 late). During taxi out; #2 DEU failure caused a return to the terminal. After maintenance was performed; the aircraft blocked out for the second time at XD:36 (2:46 late). Ground control cleared us to taxi to Runway XXL and [along the route hold at] Taxiway X. Taxiway X and Taxiway Y are both at the approach end of runway XXL with open tarmac between them. Taxiway Y is nearest the beginning of the runway. Also; there is a flange on the west end of Taxiway Y to facilitate a high-speed turn off from runway XYR. The width of the widest part of this flange is approximately equal to the runway width.Approaching hold point Taxiway X; tower instructed us to hold short of holding point Taxiway Y. There was a wide-body aircraft holding at Taxiway X; which was subsequently cleared for takeoff. As that aircraft was rolling for takeoff; we were instructed to taxi into position and hold. We entered the runway area via holding point Taxiway Y. A yellow runway exit line curved to the right toward the runway centerline from hold point Taxiway Y. Hold point Taxiway X was to the left; which allowed the full length of the runway. We expected full length. There was open tarmac between these two runway entrances; so we turned about 45 degrees left to maneuver the aircraft to a position closer to the beginning of the runway. When the aircraft was turned right to align with the runway; the yellow line leading to the runway centerline was not evident and the right runway-edge line was mistaken for the runway centerline. The captain set the brakes and transferred aircraft control to the first officer. During the turn to the right to align the aircraft; the first officer was scanning for possible malfunctions associated with the multiple maintenance issues leading up to this point. After transfer of aircraft control; I noticed there was a notable lack of runway markings in this hold position. In my mind; this was attributed to being on an open ramp area prior to the beginning of the runway. I expected normal runway markings to be just ahead. A lack of familiarity with this runway and the large open tarmac between the hold-short area and the runway contributed to this misperception. After receiving takeoff clearance and during the initial part of the takeoff roll; the first officer's attention was inside focused on setting takeoff power. During this time; the aircraft was aligned with the right-side runway edge lights. As the flange narrowed from right to left to meet the edge of the runway; it became apparent that the centerline was to the left. With rudder pedal steering; the aircraft was maneuvered to the left to join the centerline. The maneuvering occurred after setting takeoff power and runway centerline was achieved just prior to 100 knots. All maneuvering was in the low-speed regime and it was not apparent that we impacted any runway lights during the takeoff roll. We elected to continue the takeoff. The remainder of the flight was uneventful. After blocking in at ZZZZ1; we discovered that one of the nose wheels sustained notable damage to its sidewall. While taxiing the aircraft onto the runway for takeoff; B-737 crew was unable to see the yellow line leading to the runway centerline and mistook the right runway-edge line for the runway centerline. Crew recognized the error; corrected to centerline by 100 knots and continued the takeoff. On post-flight inspection the crew discovered damage to the nose wheels sidewalls.